ODE
\[ 2 f(x)^2 y''(x)=f(x) y'(x) \left (3 f'(x)-2 f(x) y(x)\right )+f(x) y(x)^2 f'(x)+y(x) \left (f(x) f''(x)-2 f'(x)^2-2 f(x)^3\right )+2 f(x)^2 y(x)^3 \] ODE Classification
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Book solution method
TO DO
Mathematica ✗
cpu = 0.742383 (sec), leaf count = 0 , could not solve
DSolve[2*f[x]^2*Derivative[2][y][x] == 2*f[x]^2*y[x]^3 + f[x]*y[x]^2*Derivative[1][f][x] + f[x]*(-2*f[x]*y[x] + 3*Derivative[1][f][x])*Derivative[1][y][x] + y[x]*(-2*f[x]^3 - 2*Derivative[1][f][x]^2 + f[x]*Derivative[2][f][x]), y[x], x]
Maple ✓
cpu = 7.902 (sec), leaf count = 121
\[\left [y \left (x \right ) = 0, y \left (x \right ) = \sqrt {f \left (x \right )}, y \left (x \right ) = -\sqrt {f \left (x \right )}, y \left (x \right ) = \RootOf \left (-63 \left (\int \sqrt {f \left (x \right )}d x \right )-\left (\int _{}^{\textit {\_Z}}\frac {4 \RootOf \left (\left (-4 \textit {\_f}^{6}+12 \textit {\_f}^{4}-12 \textit {\_f}^{2}+320 \textit {\_C1} +4\right ) \textit {\_Z}^{9}+\left (-189 \textit {\_f}^{6}+567 \textit {\_f}^{4}-567 \textit {\_f}^{2}+15120 \textit {\_C1} +189\right ) \textit {\_Z}^{6}+238140 \textit {\_C1} \,\textit {\_Z}^{3}+1250235 \textit {\_C1} \right )^{3}+63}{\textit {\_f}^{2}-1}d \textit {\_f} \right )+63 \textit {\_C2} \right ) \sqrt {f \left (x \right )}\right ]\] Mathematica raw input
DSolve[2*f[x]^2*y''[x] == 2*f[x]^2*y[x]^3 + f[x]*y[x]^2*f'[x] + f[x]*(-2*f[x]*y[x] + 3*f'[x])*y'[x] + y[x]*(-2*f[x]^3 - 2*f'[x]^2 + f[x]*f''[x]),y[x],x]
Mathematica raw output
DSolve[2*f[x]^2*Derivative[2][y][x] == 2*f[x]^2*y[x]^3 + f[x]*y[x]^2*Derivative[1][f][x] + f[x]*(-2*f[x]*y[x] + 3*Derivative[1][f][x])*Derivative[1][y][x] + y[x]*(-2*f[x]^3 - 2*Derivative[1][f][x]^2 + f[x]*Derivative[2][f][x]), y[x], x]
Maple raw input
dsolve(2*f(x)^2*diff(diff(y(x),x),x) = f(x)*(3*diff(f(x),x)-2*f(x)*y(x))*diff(y(x),x)+(f(x)*diff(diff(f(x),x),x)-2*diff(f(x),x)^2-2*f(x)^3)*y(x)+f(x)*diff(f(x),x)*y(x)^2+2*f(x)^2*y(x)^3, y(x))
Maple raw output
[y(x) = 0, y(x) = f(x)^(1/2), y(x) = -f(x)^(1/2), y(x) = RootOf(-63*Int(f(x)^(1/2),x)-Intat((4*RootOf((-4*_f^6+12*_f^4-12*_f^2+320*_C1+4)*_Z^9+(-189*_f^6+567*_f^4-567*_f^2+15120*_C1+189)*_Z^6+238140*_C1*_Z^3+1250235*_C1)^3+63)/(_f^2-1),_f = _Z)+63*_C2)*f(x)^(1/2)]